These ten colours make up the iOS 7 system palette, true to their exact red, green and blue values. In an effort to avoid a fragmented aesthetic, Apple has encouraged a careful approach to selecting colours to use in iOS 7 app interfaces.
This strict palette is used across glyphs and text. It is focused on four primary system colours: red, green, blue and grey (arguably a shade), with others present to fill the spectrum.
Since we are asked to refer to this centralised colour palette, I've generated these into Photoshop colour swatches to avoid any arbitrary selections. I've referred to Chirag Mehta's Name that Color to name the six non-system colours (using the closest available titles), as well as including system apps that have implemented each colour for reference.
The values to generate the swatches were obtained from a WWDC 2013 Session Video.